The Preliminary Idea
Working theory behind the nozzle
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With iteration 3 completed, and iteration 4 theoretical calculations started, we stumbled upon a conundrum. As the air exits the duct, the stream of air that is formed by the blower and duct is quickly dissipated into the atmosphere. This led the team to ask the question "how can we increase the effective distance at which the airflow can maintain the necessary velocity to knock down a mesquite bean?" The solution was a nozzle.
The idea of reducing the cross-sectional area of the outlet following the mass continuity equation would theoretically increase the velocity of the system which would increase the distance that the system could maintain the effective velocity of 19.5mph. |
Nozzle Iteration 1
The following nozzles blower were attached to the iteration 3 setup and analyzed in order to determine what shape would have the best performance. The results are shown in the graph below. All nozzles would have an inlet diameter of 6in and an outlet diameter of 3in.
Results of nozzle iteration 1
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First Iteration nozzles straight, concave, and converging diverging from left to right
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According to our testing, the straight and concave nozzles both preformed better than the blower by itself. The difference between the straight and concave nozzles were negligible so we decided to proceed with the straight nozzle for iteration two due to it being easier to print.
Parametric Nozzle Analysis
With a general nozzle geometry in mind, the team could then move forward to modeling the nozzle with the parameters in iteration 4. The nozzle will increase in size with an inlet diameter of 12in and outlet diameter of 6in. The nozzle was then modeled in solid works and ran through a parametric simulation.
Parametric Setup
Nozzle length formula with respect to theta
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To best determine the geometry of the nozzle with the stated nozzle inlet and outlet dimensions above, a parametric computational fluid dynamic study was run to determine the optimal length of the nozzle. Nozzle length was the only thing that was considered because the fluid velocity within the nozzle can be considered incompressible (Mach speed is less than 0.3).
To run the study, the following analysis of nozzle shape was created. For each increase in nozzle length, the angle at which the wall slopes towards the outlet approaches 90 degrees with respect to the inlet of the nozzle. This can be used to develop a relationship between the length of the nozzle and the angle of the nozzle wall. This angle would become the driving value in the simulation studies that where ran. The equation shows the relationship between the nozzle length and the angle of the wall used to create the parameters of the computational fluid dynamic study. |
This equation can then be used to find the volume of the nozzle. To determine the volume, a cone with a radius of 6.25 inches and the length of the outside nozzle can be subtracted from a cone with a radius of 6 inches and the length of the inside nozzle. Then a third cone can be subtracted from hollow cone volume by utilizing a relationship between the radius and angle at which the cone wall is sloping. This is described with the following equations.
Nozzle Volume formula with respect to theta
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The following table shows the different design points that were analyzed for the fluid dynamic simulations. These design points range from 1.15 rad to 1.45 rad with 40 increments. This was then used to determine the nozzle characteristics to inform nozzle selection.
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Design Parameters for testing
Parametric Computational Fluid Dynamics
The concept of parametric computational fluid dynamics (CFD) came with the question on how would the velocity of air be effected by the nozzle length. To explore this a simulation with the parameters mentioned above as well as duct exit conditions of iteration 3 would be used. The tackled was how would the shape of the nozzle effect the output.
Mesh of each design point
Cut plots of each design point
Flow Trajectories of each Design Point
The results of the simulation showed an increase in velocity as the length of the nozzle increases, but with increased length more material has to be used to achieve the desired shape. This led the team to graph the output velocity of each design point along with the weight of each nozzle.
Nozzle Length and Weight Graph dependent on Length
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The chart shows how the nozzles output velocity increases with distance, but also shows that the expected weight of the nozzle will also increase. The team decided to choose a nozzle between 10in and 15in. Any nozzle below 10in would not provide an adequate output and any nozzle above 15in would not have an output velocity high enough to justify the extra weight of the system.
For the nozzle that will go on the final product the team decided that we will go for a 10in nozzle with the 12in diameter inlet and 6in diameter outlet. |
The Straight Nozzle
 Straight nozzle experimental results following iteration 4
With the simulations done, the team went on a designed a new straight nozzle that would be approximately 12in long and with a 12in diameter inlet and 6in diameter exit. The velocity of the nozzle ended up in the range of 50mph at the exit. The nozzle didn't preform as well as the simulations would suggest due to the back pressure created within the system.
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Straight nozzle experimental results in graphical form
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The 5th Order Nozzle
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With the nozzle preforming optimally, we took it to midterm presentations ready to present our findings. The midterm presentation gave us insightful information from Dr.Choutapalli to create a 5th order polynomial curved nozzle. The suggestion drove the team to another parametric nozzle with a curve. The question to ask was how does the curve effect the velocity output. A general shape was informed through a paper that analyzed geometry of water jet nozzles through the use of similitude. The results shows that the experimental model can theoretically replicate the actual nozzle for our purposes and dimensions. The paper recommends a converging angle of 15 degree between the inlet and outlet. We determined that adding a curve will allow a smooth transition and increase our velocity output. Below shoes the parametric results.
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Similitude Calculations based on paper
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5th Order Simulation Results
This graph shows the expected outlet velocity for each iteration. There was no clear trend, but design point 6 shows a good velocity output that was higher than that straight nozzle simulation as well as a geometry that was easily manufacturable through 3d printing. This nozzle and the results can be found in the final iteration.
Frame Iterations
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This is iteration 1 of the frame that was designed. The frame was constructed out of steel which made it heavy which was put into consideration for the final design. Furthermore, the frame contained sharp edges which proved to be hazardous to the end user. This iteration would inform us that the material used would be crucial to the structual integrity of the system, but as well as the comfort for the end user.
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The second frame iteration used aluminium to create a U-shaped frame out of aluminum in order to minimize weight and parts that could potentially injure the end user. When tested the proposed frame was strong, but failed during testing due to the stress concentration created by the hole where the pole would be inserted. The design would be optimized to the final iteration by adding two washers where the pole and frame meet and the the nut and pole attached too. This would increase the structural integrity of the system allowing the end user to safely utilize the system.
Cracked frame due to stress concentration
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Final frame assembly
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This is the final frame iteration (in black) that is on the final product. The black frame was painted to provide a protective coating and the there are two washers that help distribute the stress on along the frame and away from the hole.
Final frame compared to third frame
